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Homework Help: Rigid body energy and spring

  1. Jan 13, 2010 #1
    hi, i'll be glad to get some help with that.
    thanks

    A thin uniform rod has mass M = 0.5 kg and length L= 0.55 m. It has a pivot at one end and is at rest on a compressed spring as shown in (A) in the attached image. The rod is released from an angle θ1= 63.0o, and moves through its horizontal position at (B) and up to (C) where it stops with θ2 = 105.0o, and then falls back down. Friction at the pivot is negligible. Calculate the speed of the CM at (B).
    The spring in (A) has a length of 0.11 m and at (B) a length of 0.14 m. Calculate the spring constant k.

    I will combine that two mandatory fields as i dont understand the first of them.
    In general i see that the first question is an energy conservation question.
    i can use the second and third state to find the speed.
    so i write an equation where the potential energy of state c equals the kinetic energy of state b, in case i choose the zero line to where the rod is parallel to the ground.
    what i don't know is how to treat the potential energy. i know that the kinetic one
    consists of the c.m part and the 0.5Iw^2 part but what about mgh, different parts of the rod are in different hights?

    thanks
    and sorry if i wasn't totally formal, i just didn't know how to
     

    Attached Files:

  2. jcsd
  3. Jan 13, 2010 #2

    tiny-tim

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    Welcome to PF!

    Hi zhenyazh! Welcome to PF! :smile:

    (have an omega: ω :wink:)

    Yes, it's an energy conservation question.

    For the gravitational PE, only the position of the centre of mass matters, so in mgh use h as the height of the centre of mass. :smile:
     
  4. Jan 13, 2010 #3
    thanks
    can u help me out with the second part too? i just get confused with the equations
     
  5. Jan 13, 2010 #4

    tiny-tim

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    You mean "The spring in (A) has a length of 0.11 m and at (B) a length of 0.14 m. Calculate the spring constant k." ?

    Again, use conservation of energy …

    at maximum compression, the KE of the rod is zero.

    What do you get? :smile:
     
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